Credit card transaction would fail, as most if not all online transactions require your billing zip code to verify the credit card.
No I would say this happened but rarely.
Million and millions of transactions a day, practically all services bought online are not affected by address, and a heck of a lot of shipped purchases ARE to addresses other than CC address.
I just bought downloaded anti virus software, if it was on a stolen credit card the vendor and CC issuer would not know. My business is a service business and I often sometimes send gifts to to physical addressed not associated with me whatsoever.
My kids' grandmother lives overseas and can go on US amazon, order and ship to my kids. I actually recently ordered shipped two doors to a classic car to an extra space storage office place in Virginia with the addressee the manager of the place, billed to my Amex
Very rarely I have will gotten a small delay, or fraud alert call from credit card companies, where they call and confirm I ordered, but that is it.
Credit and debit card companies, and larger vendors, have huge data sets and very advanced algorithms to look for known patterns to predict fraud risk. Certainly no address needed or a different address are factors that contribute, but it is likely one of several needed to trigger a payment delay and call to you